A controversy is a dispute -- a disagreement about which parties are actively arguing. Controversies can range from a private disputes between two individuals to the largest social upheavals.
"Controversial" may be recognized as a self-fulfilling adjective, which, whenever the reader sees it, should be critically scrutinized:
"Andrew Mellon, the American banker..."
"Andrew Mellon, the controversial American banker..."
Propagandists characteristically employ "Controversial" as a "tar-brush," pejoratively to identify a subject and thus create a perceived atmosphere of controversy, where perhaps none authentically exists:
"Beatrix Potter's creation, Peter Rabbit..."
"Beatrix Potter's controversial creation, Peter Rabbit..."
It should be kept in mind that some quite genuine controversy is actually confined to a fanatical fringe element.